Levi-curvature of manifolds with a Stein rational fibration

1985 ◽  
Vol 50 (1) ◽  
pp. 269-311 ◽  
Author(s):  
H. Azad
Keyword(s):  
Rational Fibration ◽  
Levi Curvature

scholarly journals Higher codimensional foliations with Kupka singularities

2017 ◽  
Vol 28 (03) ◽  
pp. 1750019
Author(s):  
O. Calvo-Andrade ◽  
M. Corrêa ◽  
A. Fernández-Pérez
Keyword(s):  
Normal Form ◽  
Positive Integer ◽  
Projective Space ◽  
Complete Intersection ◽  
Holomorphic Foliations ◽  
Connected Component ◽  
Codimension One ◽  
Dimension Formula ◽  
Rational Fibration

We consider holomorphic foliations of dimension [Formula: see text] and codimension [Formula: see text] in the projective space [Formula: see text], with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration [Formula: see text]. As a corollary, if [Formula: see text] and has a transversal type diagonal with different eigenvalues, then the Kupka component [Formula: see text] is a complete intersection and the leaves of the foliation define a rational fibration. The same conclusion holds if the Kupka set has a radial transversal type. Finally, as an application, we find a normal form for non-integrable codimension-one distributions on [Formula: see text].

scholarly journals A Jellett type theorem for the Levi curvature

2017 ◽  
Vol 108 (6) ◽  
pp. 869-884 ◽  
Author(s):  
Vittorio Martino ◽  
Giulio Tralli
Keyword(s):  
Type Theorem ◽  
Levi Curvature

Nonsmooth hypersurfaces with smooth Levi curvature

2013 ◽  
Vol 76 ◽  
pp. 115-121 ◽  
Author(s):  
Cristian E. Gutiérrez ◽  
Ermanno Lanconelli ◽  
Annamaria Montanari
Keyword(s):  
Levi Curvature

scholarly journals GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON ℂℙ2 OF DEGREE 2

2010 ◽  
Vol 53 (1) ◽  
pp. 153-168 ◽  
Author(s):  
CLAUDIA R. ALCÁNTARA
Keyword(s):  
Moduli Space ◽  
Invariant Theory ◽  
Geometric Invariant Theory ◽  
Del Pezzo Surfaces ◽  
Holomorphic Foliations ◽  
Geometric Invariant ◽  
Linear Action ◽  
Unstable Foliation ◽  
Rational Fibration ◽  
Del Pezzo

AbstractLet 2 be the space of the holomorphic foliations on ℂℙ2 of degree 2. In this paper we study the linear action PGL(3, ℂ) × 2 → 2 given by gX = DgX ^(g−1) in the sense of the Geometric Invariant Theory. We obtain a characterisation of unstable and stable foliations according to properties of singular points and existence of invariant lines. We also prove that if X is an unstable foliation of degree 2, then X is transversal with respect to a rational fibration. Finally we prove that the geometric quotient of non-degenerate foliations without invariant lines is the moduli space of polarised del Pezzo surfaces of degree 2.

scholarly journals Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature

2002 ◽  
Vol 188 (1) ◽  
pp. 87-128 ◽  
Author(s):  
G. Citti ◽  
E. Lanconelli ◽  
A. Montanari
Keyword(s):  
Lipschitz Continuous ◽  
Levi Curvature

scholarly journals Geometric Properties of Solutions of the Levi Curvature Equation in C2

1996 ◽  
Vol 138 (1) ◽  
pp. 188-212 ◽  
Author(s):  
Zbignew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Geometric Properties ◽  
Curvature Equation ◽  
Levi Curvature
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